In digital telecommunications systems and in particular in telecommunications systems of a wireless type, there are often encountered transmission channels with memory. Said transmission channels with memory bring about a spread in time of the transmitted signal. In the frequency domain, said phenomenon produces the so-called frequency selectivity. It is crucial in these cases to know the amount of said spread, which is often characterized by a so-called delay-spread time. The knowledge of the delay spread enables among other things adaptive calibration of the channel-estimation algorithms. Said algorithms must estimate a number of parameters proportional to the delay spread. In the case where this is unknown, the channel estimators must be parameterized in a conservative way, e.g., presupposing always having the maximum delay spread that can be supported by the system. Said assumption has as an effect a reduction in the overall performance of the system.
In greater detail, a transmission channel with memory is characterized by an impulse response h(τ) of the type:
                              h          ⁡                      (            τ            )                          =                              ∑                          i              =              0                                      L              -              1                                ⁢                                    h              i                        ·                          δ              ⁡                              (                                  τ                  -                                      τ                    i                                                  )                                                                        (        1        )            where hi indicates a complex number (which is possibly time variant) that represents a gain applied to the replica of the received signal with a delay ti, and L represents the number of distinguishable replicas. The gains hi are complex Gaussian random variables with zero mean. In some cases the gain h0 can have a mean other than zero. Said channels are referred to as Rice channels.
A corresponding transfer function H(ƒ) of the impulse response h(τ) of the transmission channel with memory is obtained by applying the Fourier transform:
                              H          ⁡                      (            f            )                          =                                            ∫                              -                ∞                                            +                ∞                                      ⁢                                                            h                  ⁡                                      (                    τ                    )                                                  ·                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    f                    ⁢                                                                                  ⁢                    τ                                                              ⁢                                                          ⁢                              ⅆ                τ                                              =                                    ∑                              i                =                0                                            L                -                1                                      ⁢                                                            h                  i                                ·                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    f                    ⁢                                                                                  ⁢                                          τ                      i                                                                                  ⁢                              ⅆ                τ                                                                        (        2        )            A power delay profile (PDP), P(τ), is defined as:
                              P          ⁡                      (            τ            )                          =                              ∑                          i              =              0                                      L              -              1                                ⁢                                    E              ⁡                              [                                                                        h                    i                    2                                                                    ]                                      ·                          δ              ⁡                              (                                  τ                  -                                      τ                    i                                                  )                                                                        (        3        )            where for reasons of simplicity
            ∑              i        =        0                    L        -        1              ⁢          E      ⁡              [                                        h            i            2                                    ]              =  1.
Defined as mean square deviation of the delay spread, or root mean square delay spread (RMS-DS) and designated by τrms is the following quantity:
                              τ          rms                =                                                            ∑                i                            ⁢                                                                                                              h                      i                                                                            2                                ⁢                                  τ                  i                  2                                                      -                                          (                                                      ∑                    i                                    ⁢                                      (                                                                                                                                                  h                            i                                                                                                    2                                            ·                                              τ                        i                                                              )                                                  )                            2                                                          (        4        )            
The RMS-DS τrms provides a quantitative measurement of the degree of delay spread produced by the channel. Its inverse provides, instead, a measurement of the coherence band of the channel itself. This represents the bandwidth that incurs the same type of distortion by the channel. It is evident that the greater the dispersion of the channel the smaller will be the coherence band and consequently the more the channel will be selective in frequency.
The knowledge of the RMS-DS τrms hence indirectly provides a tool for selecting the unknown parameters of the impulse response h(τ) or of its transform H(ƒ); for example, assuming a delay profile P(τ) of an exponential type it is possible to obtain an estimation of the maximum significant delay tL−1.
Among the solutions known in the state of the art, the most common method for parameter estimation in OFDM systems is the one proposed in the publication O. Edfors, M. Sandell, J. van de Beek, S. K. Wilson, P. Berjesson, “OFDM Channel Estimation by singular value decomposition”, IEEE Transactions on Communications, vol. 46, No. 7 July 1998, where in particular singular-value decomposition of the correlation matrix of the channel frequency response is used. In this case, the computational cost is significant. Likewise, in O. Simeone, Y. Bar-Ness, U. Spagnolini, “Subspace-tracking methods for channel estimation in OFDM systems”, IEEE Transactions on Wireless Communications, vol. 3, no. 1, January, 2004, estimation of the rank of the correlation matrix of the channel transfer function is exploited. Also in this case, the computational costs are other than negligible.
Another technique regarding estimation of the RMS-DS τrms is proposed in the publication Wu S., Bar-Ness Y., “OFDM Channel Estimation in the presence of frequency offset and phase noise”, IEEE International Conference on Communications, ICC '03, Volume 5, May 11-15, 2003, and envisages using an iterative technique for the search for the optimal length of the channel delay profile. The technique comprises seeking the support of the channel delay profile (which is proportional to the delay spread) increasingly from 1 to the length of the cyclic prefix of the OFDM symbol. At each iteration, two conditions are verified, which compare the improvement obtained in the estimation of the delay profile with respect to the previous iteration. The length of the support is determined from the outcome of the two comparisons. The latency and computational costs of this approach are evident.
A method for estimating the delay-spread value is known from the publications: K. Witrisal, Y. Kim, R. Prasad, “A new method to measure parameters of frequency-selective radio channels using power measurements”, IEEE Transactions on Communications, vol. 49, No. 10, October 2001; and K. Witrisal, “On estimating the RMS Delay Spread from the frequency domain level crossing rate”, 2001, IEEE Comm. Letters, Vol. 5, No. 7, pp. 3366-3370. Said method is based upon the proportionality between the density of crossings of the envelope of the channel transfer function with a pre-selected level and the RMS-DS τrms itself. The method described in the above documents has been developed in a context of statistical characterization of radio channels in order to provide designers of wireless telecommunications systems with realistic channel models. Said method, however, involves pre-selecting an adequate level and is sensitive to noise.